Real Fuzzy Math

[rjclayton]

@Jennifer:

@rjclayton:

@Jennifer:

Neutral to most people is better then negative, and thus is good.  Even the number ZERO is considered a positive number (which is why there is not a negative sign on it.)  And before anyone speaks, yes, there is such a thing as -0.  It is approaching zero from the left (ie as the negative numbers increase in value towards zero.)

Sigh Why do I let myself get sucked into this?

Actually, zero is neither a negative or a positive number.
http://mathforum.org/library/drmath/view/58735.html

This is technically off topic.  I could list an entire library of sources that go into how zero really does have polarity.  But I’ll sum it up pretty and pink:  The link you refrence is a blogger who is attempting to assist grammer and secondary school students and thus, dumbs down the responses to their level.  However, in more esoteric mathematics, you find out that zero really does have a polarity but +0 is equal to -0.  The difference comes into play when you are trying to denote from which direction you are comming from.  It may seem trivial, but the square root of negative one seemed trivial at one time as well.  As did the acceleration due to gravity constant, the speed of light, and all other mathematical break throughs.

Anyway, long, LONG story short, zero has polarity.  But in fundamanetal mathematics, it’s unneeded and thus, you are told that there is no need to denote the polarity.  After all, at your level of mathematics (you= plural) a zero is a zero.  If you are dividing by it, you have n assymptote.  If you are multiplying by it, you have negated the coefficients and products of that zero.

[Guest]

Yeaaaaaaaaaaaa……that is pretty dumb.

[ajgundam5]

@Mechanized:

Yeaaaaaaaaaaaa……that is pretty dumb.

:lol:

[Jennifer]

Dumb or not, it’s true.

And no, you are not going to debunk millenia of mathematics by quoting some guy with a blog who’s entire goal is to help lesser mathematicians along with rudimentary functions.

[Guest]

Yeaaaaaaaaaaaaaaaaaaaaaaaa….

…its pretty dumb.

[rjclayton]

How about instead of listing an entire library of resources you could think about just listing one source supporting your argument?

[Jennifer]

@rjclayton:

How about instead of listing an entire library of resources you could think about just listing one source supporting your argument?

I’ll do you one better, I’ll just give you an example.  Otherwise I have to start pulling down math tomes and getting ISBN numbers, then you have to go buy them to check if I am right or not.  (Since the library won’t have them, and I highly doubt you have them, not focusing on theoretical, pure mathematics.)

Lim f(x)
X–> 0

f(x) = (1)/(x)

Here we have a vertical asymptote.  As you know, you technically cannot divide by zero, but you can approximate.  In this situation you have a result of both positive infinity and negative infinity.  But how do you determine which is really your true answer?  Well, you need to know the polarity of the zero.  Is it positive, or is it negative?  If zero is negative, which means you are approaching from the left, then your answer is negative infinity.  If zero is positive, which means you are approaching from the right, then your answer is positive infinity.

There are other examples where the polarity of zero is important, but this is one most of you will understand - or so I hope.

Anyway, this just shows you, just because you don’t know something, does not mean it is wrong.  There are, in fact, many things in theoretical mathematics which are glossed over or simply omitted when instructing younger, less experienced minds so as to avoid confusing them.  Just as first aid glosses over and omitts many medical issues that the first aid student may face, in an effort to insturct without over complicating the issues.

[rjclayton]

I don’t buy your example.  Sure you can approach 0 from both the -ve or +ve side.  But it would be written like this:

Lim f(x)
x -> 0-

or this

Lim f(x)
x -> 0+

Still doesn’t mean 0 is positive or negative.  Next example please.  Or a souce would still be preferred, as requested.

[Jennifer]

Phenomenology, Logic and the Philosophy of Mathematics
Richard Tieszen
ISBN 0521837820

Essay #3

Varieties of Constructive Mathematics
Douglas S. Bridges, Fred Richman
ISBN 0521318025

Lecture Note #79

How to Read and Do Proofs: An Introduction to Mathematical Thought Processes
Danial Solow
ISBN: 0471680583

Page 179

Just three I have sitting on my shelf.

You are correct on your notation, however, you are incorrect as to your interpretation OF ZERO.  Zero is a non-number, it is a placeholder.  While your interpretation would be valid if we were approaching the asymptote at any real number, it is incorrect when we are dealing with Zero.

Zero is like infinity in that it is very difficult to play with accurately.  It has its own set of rules and regulations.  Now, most of those can be totally ignored when you’re doing something as generic as building a skyscraper, launching a rocket, etc.  However, in pure, theoretical, mathematics - the language of the universe, IMHO - those rules do bear an impact.

Remember, rules had to be invented to allow you to find real solutions for answers containing the square root of -1, same with division by zero, same with handling answers where literally, the answer is both negative infinity and positive infinity.

In my, overly simplified, example, you determine which polarity of infinity you are approaching by determining which polarity of zero you are dividing by.  That will tell you from which direction you approach infinity/negative infinity.

Yes, an instructor would probably tell you with a superscript + or -; but in real mathematics you do not have a professor to just tell you if you approach from the left or the right, you have to determine that yourself.  You can most easily determine that by determining if zero is positive or negative. (did you add to get to zero, then it is negative; did you subtract to get to zero, then it is positive.)

[Guest]

Zero is a real number, not a placeholder.
The set of real numbers includes zero.
The set of real numbers includes all numbers that are not imaginary (negative square roots)

Definition of a negative number:
A number with a value LESS THAN zero

Definition of a non-negative number:
A number with a value GREATER THAN OR EQUAL TO zero

Zero is NOT a negative number since by definition it is non-negative

[ajgundam5]

I don’t understand how negative numbers even exist … they are not a reality they are only created in math.
You cannot have a negative of something

[cystic crypt]

@AJGundam:

I don’t understand how negative numbers even exist … they are not a reality they are only created in math.
You cannot have a negative of something

so all of that debt i had didn’t exist?  What the hell was i working so hard to pay off???

[Guest]

Thats perhaps the ONLY time you can use a negative number in the real world……when you are in debt…when you owe someone an amount of something.  Other than that…you cant really have a negative number of anything.

[Guest]

temps below freezing are negative numbers
debt is the use of negative numbers
elevation below sea level is a negative
trim plane angles on a submarine can be negative degrees

Lots of usages in the everyday world…

[ajgundam5]

-Temps below freezing are made up…if you use Kelvin which actually measures from absolute zero you cannot get below 0º
-Debt shows how much money you owe someone…you don’t actually have negative money
-elevation below sea level (oxymoron?) is just how far you are below it but putting a negative sign in front of it to show that you are below not above there…you can’t be negative feet above something you are just below it
-no clue what trim plane angles are

[Guest]

Virtually all math is representative.

My point was only to show where those representations are used in every day life.

(and trim plane angle is the slope of the fins on a submarine that help the submarine change depth in the water.  A positive trim angle makes the sub rise, a negative angle makes the sub move deeper, unless I have that backward, but you get the idea).

[Jennifer]

I’m not going to get into a debate about the function of zero with a man who’s highest level of math was maybe Calculus II.  Sorry.  But you just don’t have the ground work to have the debate.  Come back after you take Multilinear Equations and Logic I and II.

Point is, zero has polarity.  It’s almost always inconsequential, but for every number and placeholder, there is a mirror image of that number or placeholder - even for zero.  It’s just irrellevant until you get to limits, and then it’s limited rellevance and then irrellevant again until you get up to multiple vectors on multiple dimensions/planes.  I’m sure there’s math above me where it’s even MORE rellevant.

Math, unlike some other areas of study, will never be complete.  There’s always some problem that needs to be fixed, sometimes we do that with imaginary numbers, sometimes with polarity and sometimes with rudimentary and very crude PEMDAS functions.

[Jermofoot]

Zero is the absence of value, therefore not positive or negative - just read what Switch said.

Although, I don’t think there are negative or positive numbers (IMO) - that’s all a point of reference.

[Jennifer]

@Jermofoot:

Zero is the absence of value, therefore not positive or negative - just read what Switch said.

And in lower level math you can negate the polarity of zero, it actually makes lower level math much simpler and easier for beginning mathematicians to understand.  But just because you ignore something does not mean it does not exist.

For instance, 1/x when x=0 is said to be undefined.  Technically true.  Literally not.  y= infinity and negative infinity at that point and so, since a function cannot have two outputs for one imput, they have to figure out WHY it has two outputs.  The answer?  You had two inputs.  +0 and -0.  But for algebra and trigonometry and calculus I, II and III it’s much simpler to keep the students from being confused and just tell them that the answer is undefined.

[rjclayton]

I understand what you’re saying, but I thought that issue was solved with limits ie. like in my earlier post:

lim 1/x = - infinity
x -> 0-

lim 1/x = + infinity
x -> 0+

when x=0:
1/(0) = undefined

So there is actually no value for the function when x=0 (rather than 2 values as you claim).

Or does higher math undo these teachings and replace with new teachings as you claim?  dun dun dun!